Troy Mahon What is a Maze An intricate usually confusing network of interconnecting pathways the Free Dictionary Many different kinds Not all mazes can be solved the same way Brief History ID: 339797
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Slide1
Solving Mazes
Troy MahonSlide2
What is a Maze?
“An
intricate, usually confusing network of interconnecting
pathways…” (the Free Dictionary)
Many different kinds
Not all mazes can be solved the same waySlide3
Brief History
Goa, India… 4,000 years ago…
Classical Labyrinth circleSlide4
Brief History (Cont.)
"It is a confusing path, hard to follow without a thread, but, provided [you are] not devoured at the midpoint, it leads surely, despite twists and turns, back to the beginning." — Plato
c. 400 BCESlide5
Different Types of Mazes (Routing)
Mazes vs. Labyrinth
Labyrinth have no dead ends and usually don’t require choices
One continues winding path
May or may not have dead ends
Might just loop around somewhere else (called a “braid”)
Can have different dimensions
Simply connected or not (i.e. have islands or blocked off areas)Slide6
Higher Dimensional Mazes
A 3D Maze is a 2D Maze with different levels connected by a bridge/staircase
4D will have portals leading to different levels…Slide7
Weaves and Tessellation
Weaves are similar to highway overpasses
Path can go under/over at certain place
Tessellation refers to the shape of an individual cell with a maze
Square, triangular, irregular, etc.Slide8
Algorithms to Solve a MazeSlide9
Wall Follower Method
Easiest method to employ
Take right hand, place it on wall and follow that direction
“Right hand rule”
Take Left hand, place it on wall and follow that direction
“Left hand rule”
Either will workSlide10
Pledge Algorithm
A modified wall following method
Useful with programmed robots
Can be used by a person with a compass
Need to keep track of your spatial orientation
0 degrees does not equal 360
Helps if you have a maze with a standard cell type
Doesn’t work if your trying to get to the center (only escape or go through)Slide11
Trémaux’s Algorithm
Can be used by a person in a maze
Leave a trail (bread crumbs, trace with pencil, etc.)
Follow the path until a junction
Choose one passage at random
If dead end or old junction is encountered head back to original junction and try new passage.
After finding the solution, the solution path will be only marked once
All else will either have two lines or noneSlide12
Dead-End Filler
Find the dead ends (if there are any)
Follow them to the nearest junction and close them off
When finished only one clear solution will remain
Cannot be done by someone in a mazeSlide13
Let’s Review
Wall Follower Method
Effective, easy, works (not all the time)
Pledge Algorithm
Effective but get’s confusing
Can’t get to the center from outside
Trémaux’s Algorithm
Boils down to Hansel and Gretel explorer method
When all else fails, go with this one
Dead-End FillingOnly useful from an aerial viewSlide14
Real Life Application
Someone is trapped in a maze
What do you?Slide15
Real Life Application (Answer)
If it’s a simple maze:
Use the Wall follower method
Have one person do the right hand method
Have the other do the left hand method
One of them will have found the missing person before encountering the exitSlide16
Other Considerations
Mazes can be used in Graph Theory
Different mazes pose problems to different algorithms
The definition of a maze can really be expandedSlide17
Sources Used
Google Images
http://
www.astrolog.org/labyrnth/algrithm.htm
http://
www.labyrinthos.net/typomaze01.html
http://
www.thefreedictionary.com/maze
http://
www.nbm.org/about-us/national-building-museum-online/history-of-the-maze.html